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More than three centuries have passed since the scientific revolution culminated in the outstanding achievement of Isaac Newton. During that time, human life has been transformed by science and the technology springing from it.

Yet we find ourselves in a peculiar and unstable position. As our knowledge of the physical world has advanced, our understanding of knowledge itself has lagged behind. I witnessed this gap between physics and epistemology during my college years at the University of California, Berkeley. In my physics lab course, I learned how to determine the atomic structure of crystals by means of x-ray diffraction and how to identify subatomic particles by analyzing bubble-chamber photographs. In my philosophy of science course, on the other hand, I was taught by a world-renowned professor (Paul Feyerabend) that there is no such thing as scientific method and that physicists have no better claim to knowledge than voodoo priests. I knew little about epistemology at the time, but I could not help noticing that it was the physicists, not the voodoo priests, who had made possible the life-promoting technology we enjoy today.

The triumphs of science stand as a monument to the power of reason, and they stand as a clear refutation of the skepticism that is epidemic in contemporary philosophy of science. Why then does this situation persist in universities around the world? How did we arrive at this bizarre contradiction—with scientists developing technology that exploits our detailed knowledge of atomic structure, while philosophers bewail or revel in the alleged impotence of reason to grasp even relatively simple facts?

E. Bright Wilson, who was a professor of chemistry at Harvard, once stated the problem in this way:

Practical scientists who rashly allow themselves to listen to philosophers are likely to go away in a discouraged frame of mind, convinced that there is no logical foundation for the things they do, that all their alleged scientific laws are without justification, and that they are living in a world of naïve illusion. Of course, once they get out into the sunlight again, they know that this is not so, that scientific principles do work, bridges stay up, eclipses occur on schedule, and atomic bombs go off.

Nevertheless, it is very unsatisfactory that no generally acceptable theory of scientific inference has yet been put forward. . . . Mistakes are often made which would presumably not have been made if a consistent and satisfactory basic philosophy had been followed.1

The central issue here is the failure of philosophers to offer a solution to what has been called “the problem of induction.” Induction is the process of inferring generalizations from particular instances. The complementary process of applying generalizations to new instances is deduction. The theory of deductive reasoning was developed by Aristotle more than two millennia ago. This crucial achievement was a start toward understanding and validating knowledge, but it was only a start. Deduction presupposes induction; one cannot apply what one does not know or cannot conceive. The primary process of gaining knowledge that goes beyond perceptual data is induction. Generalization—the inference from some members of a class to all—is the essence of human cognition.

When we reason from “Men in my experience are mortal” to “All men are mortal”; or from “These fires burn me when touched” to “Fire by its nature burns”; or from “This apple and the moon obey the law of gravity” to “Every physical object in the universe obeys the law”—in all such cases, we are passing from one realm to another: from the observed to the unobserved; from the past behavior of nature to its future behavior; from what we discover in a narrow corner of a vast cosmos to what is true everywhere in that cosmos. This passage is the epistemological dividing line between man and animals.

Animals are perceptual-level organisms. They learn from experience, but only by highly delimited perceptual association. They cannot imagine the unobserved, the future, or the world beyond such associations. They know, deal with, and react to concretes, and only concretes. But this is not a level on which man can live and prosper. To act successfully in the present, a human being must set long-range goals and a long-range course of action; to do so, he must know the future—perhaps months ahead, often years, sometimes decades.

A generalization is a proposition that ascribes a characteristic to every member of an unlimited class, however it is positioned in space or time. In formal terms, it states: All S is P. This kind of claim, on any subject, goes beyond all possible observation.

But man is neither omniscient nor infallible. His generalizations, therefore, are not automatically correct. Thus the questions: How can man know, across the whole scale of space and time, facts which he does not and can never perceive? When and why is the inference from “some” to “all” legitimate? What is the method of valid induction that can prove the generalization to which it leads? In short, how can man determine which generalizations are true (correspond to reality), and which ones are false (contradict reality)?

The answer is crucial. If a man accepts a true generalization, his mental contents (to that extent) are consistent with one another, and his action, other things being equal, will succeed. But if a man accepts a false generalization, it introduces in his mind a contradiction with his authentic knowledge and a clash with reality, leading unavoidably to frustration and failure in his actions. Therefore the “problem of induction” is not merely a puzzle for academics—it is the problem of human survival.